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Since you have already replaced the thermostat then other possible causes are that the R and W1 terminals in the furnace are touching somehow causing the heating mode to stay on. This can be caused by bare thermostat wires touching, thermostat wires pierced by metal somewhere, thermostat wires rubbing against sharp metal surface, or a micro relay on the furnace control board has welded itself in the "on" position requiring replacement of the control board. You can test this theory with a volt ohm meter. While in heating mode the "R" terminal and the "W1" terminal should be 24 volts AC to common(or C terminal). When heating is off "R" is 24 Volts AC and "W1" will be zero volts AC.
If you don't have a meter you could run thermostat and turn heat down so unit should shut off. While the unit is still heating remove the W1 wire from the furnace circuit board. If the heating stops you know the issue is with the thermostat wiring. If it continues then the circuit board is bad.